Trapezoid Area and Perimeter: Garden Beds, Lots, and Trench Cross-Sections
October 29, 2026
A trapezoid is a four-sided shape with one pair of parallel sides (the bases). Its area is the average of the two bases multiplied by the height: A = (a + b) ÷ 2 × h, where the height is the perpendicular distance between the bases, not the length of a slanted side.
For bases of 12 and 20 and a height of 8: A = (12 + 20) ÷ 2 × 8 = 16 × 8 = 128 square units. The formula works because a trapezoid can be rearranged into a rectangle with the average width, or split into a rectangle and two triangles.
Skip the math and get your answer instantly:
Open the Area Calculator →Perimeter of an Isosceles Trapezoid
The perimeter is the sum of all four sides. If the trapezoid is isosceles (the two slanted sides are equal), each leg forms a right triangle with the height and half the difference between the bases. With bases 20 and 12, the difference is 8, half is 4, and the height is 8, so each leg is √(4² + 8²) = √80 = 8.944. The perimeter is 20 + 12 + 2 × 8.944 = 49.89. For a non-isosceles trapezoid, measure each slanted side or use the horizontal offsets of each end with the Pythagorean theorem.
| Bases | Height | Area | Leg (isosceles) | Perimeter |
|---|---|---|---|---|
| 12 and 20 | 8 | 128 | 8.94 | 49.89 |
| 6 and 10 | 4 | 32 | 4.47 | 24.94 |
| 30 and 50 | 20 | 800 | 22.36 | 124.72 |
Garden Bed Example
A raised bed with parallel sides of 10 feet and 6 feet, and 4 feet between them, has an area of (10 + 6) ÷ 2 × 4 = 32 square feet. Filled to a depth of 8 inches (0.667 feet), it holds 32 × 0.667 = 21.3 cubic feet of soil, or 0.79 cubic yards. Divide by 27 to convert cubic feet to cubic yards. Add 5% to 10% for settling and spillage, so order about 0.85 cubic yards. If the soil is sold in 1.5-cubic-foot bags, you would need 15 bags.
Trench and Embankment Cross-Sections
A drainage trench that is 2 feet wide at the bottom, 4 feet wide at the top, and 3 feet deep has a trapezoidal cross-section of (2 + 4) ÷ 2 × 3 = 9 square feet. For a trench 50 feet long, the volume to excavate is 9 × 50 = 450 cubic feet, or 16.7 cubic yards. Road embankments, canals, and sloped-sided ditches use the same approach. Multiply the cross-sectional area by the length to find the volume.
Common Mistakes
Using the slanted side instead of the perpendicular height is the most frequent error. Mixing units (inches and feet) is another. If you know the area and one base and the height, solve for the other base with b = 2A ÷ h − a. For irregular lots, split the shape into trapezoids, triangles, and rectangles and add the areas.
Frequently Asked Questions
What is the trapezoid area formula?
(a + b) ÷ 2 × h.
Is the height the slanted side?
No. It is the perpendicular distance between the parallel sides.
How do I find the leg of an isosceles trapezoid?
Use the Pythagorean theorem with the height and half the base difference.
How do I convert cubic feet to cubic yards?
Divide by 27.
How do I find a missing base?
b = 2A ÷ h − a.